Formulas for Kepler's Laws

Towards the end of the sixteenth century, Tycho Brahe collected a huge amount of data giving precise measurements of the position of planets. Johannes Kepler, after a detailed analysis of the measurements announced three laws in 1619.

1. The orbit of each planet is an ellipse which has the Sun at one of its foci.

2. Each planet moves in such a way that the (imaginary) line joining it to the Sun sweeps out equal areas in equal times.

3. The squares of the periods of revolution of the planets about the Sun are proportional to the cubes of their mean distances from it.